An analytical investigatıon on starlikeness and convexity properties for hypergeometric functions

In this study, we analytically investigate hypergeometric functions having some properties such as convexity and starlike. We fundamentally focus on obtaining desired conditions on the parameters \ a,b\ , and $c$ in order that a hypergeometric function to be in various subclasses of starlike and convex functions of order \ \alpha=2^{-r}\ and order \ \alpha=2^{-r}\ type $\beta=2^{-1}$, with $r$ is a positive integer.